Iterative Wavefront Control Algorithm For Adaptive Optics Systems

With the rapid development of adaptive optics technology, the number of deformable mirror actuators increasingly grows, and the demand for high performance real-time wavefront processing is more and more critical. However, as is limited by the computational capability of wavefront processors, traditional wavefront control algorithms can hardly meet the growing demands. In this thesis, a series of simulations and experiments on wavefront control algorithms are made on the premise of ensuring real-time wavefront control for high-resolution adaptive optics systems.Firstly, the direct gradient wavefront control algorithm is analyzed emphasizing on the sparseness of slope response matrix, and the iterative wavefront control algorithm is adopted to make use of the sparseness of slope response matrix from deformable mirror to wavefront sensor. Iterative wavefront control algorithm employs sparse matrix vector multiplications and gets the control voltages of the deformable mirror actuators through iterations. Compared with traditional wavefront control algorithms, iterative wavefront control algorithm avoids calculating the generalized inverses matrix of slope response matrix, so the computational complexity and the occupied storage space are both decreased greatly.Secondly, based on a 979-actuator adaptive optics system, the convergences of several iterative algorithms are analyzed. Different iterative algorithms are comparatively studied according to the computational complexity and the storage space. The results show that the conjugate gradient method guarantees the lowest computational complexity and storage space. Therefore, conjugate gradient method is the best iterative wavefront control algorithm for the 979-actuator and similar adaptive optics systems.Moreover, the effectiveness of iterative wavefront control algorithm is proved.With 18 different configurations of adaptive optics systems, the iterative wavefront control algorithm and the direct gradient wavefront control algorithm are comparatively studied from the aspects of occupied storage space and computational complexity. The results show that iterative wavefront control algorithm is more suitable for adaptive optics systems with thousands of actuators, and the direct gradient wavefront control algorithm is suitable for fewer actuators. With theincreasing number of deformable mirror actuators, the computational complexity of direct gradient wavefront control algorithm grows almost exponentially with the number of actuators, while the computational complexity of iterative wavefront control algorithm is almost linear to the number of actuators.Finally, the influence of system parameters on iterative wavefront control algorithm is studied for different adaptive optics systems, including the matching relation between wavefront sensors and deformable mirrors, the coupling coefficient of deformable mirrors and the Gaussian function index of deformable mirrors. Then the optimal ranges of matching relation, coupling coefficient and Gaussian function index are provided balancing the sparseness of iterative matrix and slop response matrix, computational complexity of iterative wavefront control algorithm, correction quality and stability of adaptive optics systems.Iterative wavefront control algorithm reduces the computational complexity of wavefront control process through changing the data structure of traditional algorithm,which is especially beneficial for promoting the control bandwidth of adaptive optics systems. This research provides the criteria for selecting wavefront control algorithms for future high-resolution adaptive optics systems. The related analysis method would also aid in the design of adaptive optics systems based on iterative wavefront control algorithms.